Check force on energy

It is common practise to use the potential energy as a collective energy. Some MD codes thus pass the potential energy to PLUMED and PLUMED can then apply forces on this collective variable. We test that any forces that PLUMED applies on the potential energy are correctly passed back to the MD code by doing the following test. We first run a short simulation at $T$ K with a timestep of $\tau$ ps. During the course of this simulation we monitor the potential energy using the following PLUMED input:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e,v FILEthe name of the file on which to output these quantities=energy1

We then run a second simulation (starting from identical conditions) at a temperature of $T\alpha$ and with a timestep of $\tau/\sqrt(\alpha)$. The thermostat and barostat relaxation times are similarly divided by $\sqrt(\alpha)$. In the tests that are run on this website we set $\sqrt(\alpha)=1.1$. The PLUMED file above is used when this test is run but a different time series of energy values is recorded as the MD parameters in this second simulation are different.

If PLUMED is working correctly we should be able to recapture the time series of energy values for the first simulation by running an MD simulation with the modified parameters that were used in the second simulation and the following PLUMED input file:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
# slope is such that 
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e FILEthe name of the file on which to output these quantities=energy2
# slope should be (alpha-1)=0.21
RESTRAINTAdds harmonic and/or linear restraints on one or more variables. More details ATthe position of the restraint=0.0 ARGthe values the harmonic restraint acts upon=e SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=0.21

In other words, when forces are passed correctly the time series for the energies and volumes from the first and third of these calculations should be identical.

To determine if PLUMED passes this test we calculate the difference between the time series that were observed in the first and third simulations described above. We then divide this by the difference between the first and second time series.

An NPT version of this calculation is performed as well as an NVT calculation if the virial is passed to PLUMED.

Trajectories

  1. Input and output files for the unpeturbed calculation are available in this zip archive

  2. Input and output files for the peturbed calculation are available in this zip archive

  3. Input and output files for the peturbed calculation in which a PLUMED restraint is used to undo the effect of the changed MD parameters are available in this zip archive

Results

Original With PLUMED Effect of peturbation % Difference
-18174.8223 11.6346 -18174.8223 11.6346 0.0000 0.0000 0.0000 0.0000
-18171.8203 11.6346 -18193.2891 11.6346 6.8730 0.0000 312.3615 0.0000
-18194.2461 11.6475 -18232.5879 11.6321 22.1738 0.0054 172.9146 284.9140
-18166.7715 11.6475 -18282.8066 11.6321 17.6230 0.0054 658.4285 284.9140
-18153.8262 11.6475 -18318.9766 11.6321 19.6504 0.0054 840.4433 284.9140
-18136.0527 11.6475 -18338.5020 11.6321 20.0391 0.0054 1010.2729 284.9140
-18119.0098 11.6475 -18342.2910 11.6321 20.8242 0.0054 1072.2191 284.9140
-18108.6367 11.6475 -18337.0137 11.6321 23.7207 0.0054 962.7748 284.9140
-18108.0781 11.6475 -18330.6621 11.6321 28.7227 0.0054 774.9422 284.9140
-18116.1211 11.6475 -18328.5078 11.6321 33.8672 0.0054 627.1165 284.9140
-18127.9512 11.6475 -18331.4531 11.6321 36.4688 0.0054 558.0174 284.9140
-18138.1113 11.6475 -18337.3574 11.6321 35.2109 0.0054 565.8642 284.9140
-18144.1758 11.6475 -18344.3359 11.6321 31.7949 0.0054 629.5350 284.9140
-18148.8750 11.6475 -18353.2305 11.6321 30.9082 0.0054 661.1690 284.9140
-18158.1504 11.6475 -18366.9766 11.6321 36.6758 0.0054 569.3844 284.9140
-18175.7773 11.6475 -18386.8398 11.6321 48.4395 0.0054 435.7244 284.9140
-18198.8457 11.6475 -18409.0020 11.6321 59.1074 0.0054 355.5497 284.9140
-18218.5293 11.6475 -18425.3281 11.6321 59.5859 0.0054 347.0598 284.9140
-18225.8027 11.6475 -18428.5176 11.6321 45.6328 0.0054 444.2304 284.9140
-18217.2617 11.6475 -18417.1152 11.6321 21.3633 0.0054 935.5001 284.9140

The table below includes some of the results from the calculation. The columns contain:

  1. Time series for the energy and volume that were obtained from the simulation at $T$ K, $x_{md}$.
  2. Time series for the energy and volume that were obtained from the simulation at $\alpha T$ K and in which PLUMED applied a restraint on the energy, $x_{pl}$.
  3. The absolute value of the difference between the time series of energies and volumes that were obtained from the simulations running at $T$ K and $\alpha T$ K, $\vert x_{md}’-x_{md} \vert$. No PLUMED restraints were applied in either of these simulations.
  4. The values of $100\frac{\vert x_{md} - x_{pl}\vert }{ \vert x_{md}’-x_{md} \vert}$.

If the PLUMED interface is working correctly the first two sets of numbers should be identical and the final column should be filled with zeros.

Graphical representation (beta)

A visualization of the table above:
engvir_master